gsa industries

Case Study

GSA Industries

Submitted to:

Dr. R. Jagadeesh,

Prof. SDM IMD, Mysore.

Submitted by:

Group No. 09

Abhishek Saini (10003)

Harsh Sheth (10020)

Nargish Raman (10028)

Nikunj Patel (10029)

Sagar Bajpai (10039)

Sentil S. (10043)

Submitted as a part of the curriculum of the course Operations Research

Report On:

Operation Research Term III (2010-12)

Report On: GSA Industries Case Study

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Contents Executive summary .................................................................................. 3

Statement of the Problem/s: ................................................................... 3

Question 1: ............................................................................................... 7

Question 2 ................................................................................................ 8

Question 3:- ............................................................................................ 11

Question 4: ............................................................................................. 13

Question 5: ............................................................................................. 18

Recommendations: ................................................................................ 19

Tables and figures: ................................................................................. 20

References: ............................................................................................. 22



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Executive summary

G.S.A industries Produces four different types of prefabricated housing units at two locations: - El Cajon, California and Elkhart, Indiana. The prefabricated units are transported to regional distribution centers in Phoenix, Nashville and Miami. The organization is concerned to take decisions like which of the building at El Cajon plant should produce which model of housing unit, the optimal units to be produced in building four keeping in consideration the sub-assemblies constraints and the units to be transported to each of the distribution from the two production units. These decisions are to be made so the profit can be maximized and the cost can be minimized, as the case may be. By using the algorithm of LPP it is found that the organization can choose to produce 55 units in building 4, allocate Picket fence, Gentle stream, Town house and El president to building 1,2,3 and 4 respectively and transport all the units produced to three distribution centers, since the demand is more than the production units.

Statement of the Problem/s:

As we mentioned in executive summery GSA Industries produces four models of prefabricated housing units in each of two locations and the prefabricated housing units are transported to regional distribution centers.

With this basic information we would like to define our problem statemets...

How many Gentle Steam model can be produced in Building 4 of El Cajon Plant? These Production quantitity can be determined by analyzing the rate at which various subassemblies can be manufactures and passes along to the next operation. We have to decide production capacity by using network representation given in the case. Same is shown below.



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Figure 1: Building 4 Subassembly Capacities for Gentle Stream Model

Allocation of housing models to the buildings at El Cajon plant: • The El Cajon plant consists of four separate buildings, each of which will

produce a different model. The number of housing units which can be produced in a building depends on many factors, including the size and shape of the building and the existing production facilities.

• These allocation has to be done by maximizing the gross profits per housing model

Given table for capacity of each building is reproduced below. Table 1: building capacity for each model

Model Picked

Fence Town House Gentle

Stream El

Presidente Building 1 30 25 20 10 Building 2 60 55 50 45 Building 3 40 35 30 N/A Building 4 95 85 See text 65

25

10 60

20

20

30 15

10

50 10

40

30

Start Finished Product

1

3

6

4

2 7

5

Subassembly 2 Subassembly 1 Subassembly 3 Subassembly 4



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Interpretation of table: • If Building 1 is used to produce the Picked Fence Model- 30 such models

can be produced • If it is used to produce the Town House Model- 25 such models can be

produced.

Decide on the routes of transportation from El Cajon to distribution centers: • The unit transportation costs from El Cajon depend on the mode and time of

transportation • The cost of changing modes of transportation at a city (rail to truck, truck to

rail, or track to ship) is 250 per vehicle. Various costs are as below given in the case. Table 2: Transportation cost and time from El cajon route to Distribution centers

Shipping Routes No. of

From To Days Cost/Day Truck Routes

El Cajon Phoenix 1 $375 El Cajon Dallas 3 $300 Phoenix Rapid City 2 $250 Phoenix Oklahoma City 2 $175 Dallas New Orleans 1 $300

Rapid City Chicago 3 $325 Rapid City Oklahoma City 2 $250 Rapid City Nashville 4 $200

Chicago Nashville 2 $300 Chicago Raleigh 3 $375

Oklahoma City New Orleans 3 $225 Oklahoma City Nashville 4 $300 Oklahoma City Raleigh 5 $200

Nashville Miami 3 $350 Raleigh Miami 4 $250

Rail Routes El Cajon Phoenix 2 $250



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El Cajon Dallas 4 $350 Phoenix Rapid City 3 $175 Chicago Nashville 3 $200 Chicago Raleigh 4 $225

Oklahoma City Raleigh 3 $250 Raleigh Miami 3 $300

Boat Routes New Orleans Miami 4 $400

Transportation of units to regional distribution centers by minimizing the transportation cost: • Unit transportation charges are independent of the model shipped • We need to minimize our transportation coat so as to increase our net profit

of the year.

Concluding Problem statement:

First we need to decide on the number of units can be produced in building 4 at El Cajon plant, Based on that we need to allocate the model to buildings maximizing gross profit. (Figure 2:Consolidated diagram for all the possess and problems:)



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Decide on the route of transportation to the distribution centers from El Cajon Plant and lastly solve it as a transportation problem minimizing the cost.

QUESTION 1: Maximum production capacity of Gentle stream model at building 4 in El Cajon.

The plant is being reconfigured and the building 4 depends on the sub-assemblies in order to execute the production process. Now the sub-assembly process has different production routes. The various production lines for sub-assembly are as following:-


In the above assembly setting there are two lines emerging out of the initial point. Now the line to node one has the capacity of 30 units and further the 20 units can move to node 3 and 10 units to node 4. This is because in case we move all the 30

25

10 60

20

20

30 15

10

50 10

40

30

Start Finished Product

1

3

6

4

2 7

5

Subassembly 2 Subassembly 1 Subassembly 3 Subassembly 4



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units to node 3, there will be production congestion as the capacity to node 6 is just 20. So we move the maximum 20 units to node 3 and 10 to node 4. After this the units will move to the final node easily as the capacity is double than we need.

For the second line of production of sub-assembly, we can only move 25 units to node 2. This is because the capacity of the lines to node 4 and 5 is only 10 and 15 only. So, 10 units will move from node 4 to node 7 and 15 units from node 5 to node 7. This will cause the output of 15 units from line 2.

So the total number of units that can be produced from the sub-assembly is 55

Question 2 Which Building should produce which model at the El Cajon plant in order to maximize gross profit. (Ignore transportation costs in this analysis and discuss why this is probably valid with particular set of data. Discuss how the model would change if it were not valid)?

ANSWER:- (A)

In the previous question we determined from the network diagram of gentle stream in building 4 that we can produce 55 units of gentle stream in that building. We recreate the table below with this figure.

Table 3: building allocation after B4 allocation

Picket Fence

Town House

Gentle Stream

El Presidente

B1 30 25 20 10 B2 60 55 50 45 B3 40 35 30 0 B4 95 85 55 65

The table shows how much of each product that could be manufactured in the respective buildings B1, B2, B3 and B4. For example GSA can produce 30 units of picket fence in building B1, or 60 units in B2 and so on. We need to maximize the gross profit given the above table. It is also given that each building will produce only one product. Hence, we face an assignment problem and with the following



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given gross profit table we can find an optimum solution to assign a building to a particular product.

Table 4: Gross profit margin for all the models

Model Gross profit/unit Picket Fence $ 9,600 Town House $ 11,520 Gentle Stream $ 15,360 El Presidente $ 19,200

By multiplying the figures in Table 3 by the respective gross profit values we get the following table:-

Table 5: Total gross profit

Using Vogel’s method for maximization, the maximum gross profit we get is $ 2,707,200 and the assignments are highlighted in the table above. We summarize the assignments as follows:

Table 6: Allocation of the models to building at El Cajon Plant

Model Building Units Picket Fence B1 30 Town House B3 35 Gentle Stream B2 50 El Presidente B4 65

We have obtained the above solution using the solver on excel as well and have obtained the same solution.

Picket Fence

Town House

Gentle Stream

El Presidente

B1 288000 288000 307200 192000 B2 576000 633600 768000 864000 B3 384000 403200 460800 0 B4 912000 979200 844800 1248000



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PART (B):-

Now the question clearly mentions that while formulating the model we have to ignore the transportation costs. Now for the given set of data of Gross profit, we can ensure the validity of the model of the allocation of various types of housing units to different buildings on the basis of the L.P.P method. Now the validity can change if the figures go beyond the allowable increase/decrease, as shown in the below sensitivity report. For example, in case of Picket fence, it has been allocated to building 1 and the allowable increase is infinity so in case the Gross profit figure exceed the given amount up to infinity then the model will still hold good but since the allowable decrease is $19200 which means that if the figure of gross profit falls below this limit then the model validity will be lost and new model will have to be formulated.

Table 7: Sensitivity Analysis Report

Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease

$C$14 Fence 1 0 288000 1E+30 19200 $D$14 House 0 0 288000 19200 38400 $E$14 Stream 0 -38400 307200 38400 1E+30 $F$14 Presidente 0 -249600 192000 249600 1E+30 $C$15 Fence 0 -134400 576000 134400 1E+30 $D$15 House 0 -76800 633600 76800 1E+30 $E$15 Stream 1 0 768000 249600 76800 $F$15 Presidente 0 0 864000 115200 249600 $C$16 Fence 0 -19200 384000 19200 1E+30 $D$16 House 1 0 403200 38400 19200 $E$16 Stream 0 0 460800 76800 38400 $F$16 Presidente 0 -556800 0 556800 1E+30 $C$17 Fence 0 -182400 912000 182400 1E+30 $D$17 House 0 -115200 979200 115200 1E+30 $E$17 Stream 0 -307200 844800 307200 1E+30 $F$17 Presidente 1 0 1248000 1E+30 115200



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QUESTION 3:- The minimal total transportation costs from El Cajon to each of the distribution cities. (Discuss any time implications of your recommendations). In case of El Cajon plant of the GSA industry, the case mentions various routes that are available and the modes alternatives. There are three modes available: Truck, rail and boat. Below is the diagrammatic representation of the routes. The cost and time for the same is produced in the table 2.1 in problem statement:

Figure 3: Routes from El cajon to distribution centers (The green colored routes are selected as per minimum cost allocation.) Now on the basis of the above mentioned routes and modes we have the following alternatives available to transport the goods from El Cajon to Phoenix, Nashville and Miami. We will choose the route from plant to the distribution center which will produce the minimum cost:-



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Figure 4: All the routes cost calculation )El Cajon to Distribution centers So the minimum transportation costs are as following:- Table 8: Consolidated minimum costs of transportation from El Cajon DISTRIBUTION CENTER MINIMUM COST ($)

1. Phoenix 375 2. Nashville 1675

3. Miami 2625



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Question 4: The allocation of each housing model from each production city to each distribution city.

As now, we have decided on transportation routes and cost from El Cajon to distribution centers, we will allocate housing model to those regional distribution centers. (i.e. Phoenix, Nasville and Miami)

Transportation cost for the as per our calculations mentioned in previous question.

Table 9: Transportaion cost (El Cajon to Distribution Centers)

From /To Phoenix Nasville Miami

El cajon 375 1675 2625

Transportation cost from Elkhart to distribution centers:

Table 10: Transportaion cost (Elkhart to Distribution Centers)

From /To Phoenix Nasville Miami

Elkhart 1450 725 2500

Supply and demand data:

For El Cajon Plant (As per our calculation after allocating the models to buildings):

For Elkhart Plant (As per given in the case):

Table 11:Supply and demand data for each of the models



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Model Picket

Fence Town House

Gentle Stream

El Presidente

Phoenix 50 60 60 90 Nasville 80 60 30 20 Miami 75 90 85 90 Demand 205 210 175 200 Production at Elkhart Plant

100 75 75 120

Production at El cajol plant

30 35 50 65

Total units available (Supply)

130 110 125 185

As per the table, we can see that company is in supply deficit for all the four products (models) so for solving it as a transportation problem we need to add dummy supplier in all the cases.

Formulation for model Picket Fence:

Table 12.1: Allocation of units of Picket Fence

Picket Fence

From/To Phoenix Nasville Miami Supply

Elkhart 1450 725 2500 100

El Cajon 375 1675 2625 30

dummy supplier 99999 99999 99999 75

Demand 50 80 75 205



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As mentioned above we have created dummy supplier here which will supply 75 units. We put cost for that supplier very high so as to avoid it from the solution.

After solving it with the excel solver we got solution:


From/To Phoenix Nasville Miami Supply allocated

Elkhart 20 80 0 100 100

El Cajon 30 0 0 30 30

Dummy supplier

75 0

Demand 50 80 75 205

Allocated 50 80 0

Total cost 98250

Total cost of this transportation is coming to $98250.

We also tried it by putting constraint of Allocated demand should be less than equal to the actual demand and we got the same answer for the both procedure.

By same method we solved the problem for other three models.

Solutions for those are as follow.



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Town House:

Table 13: Allocation of units of Town House:

From/To Phoenix Nasville Miami Supply allocation

Elkhart 15 60 0 75 75

El Cajon 35 0 0 35 35

Dummy supplier

100 0

Demand 60 60 90 210

Allocation 50 60 0

Total cost 78375

Gentle Stream:

Table 14: Allocation of units of Gentle Stream:


Elkhart 10 30 35 75 75

El Cajon 50 0 0 50 50

Dummy supplier

50 0

Demand 60 30 85 175

Allocated 60 30 35

Total cost 142500



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El Presidente:

Table 15: Allocation of units of El Presidente:


Elkhart 25 20 75 120 120

El Cajon 65 0 0 65 65

Dummy supplier 15 0

Demand 90 20 90 200

Allocated 90 20 75

Total cost 262625

Table 16: Consolidated transportation cost and allocation of the models:

Elkhart El Cajon

Phoenix Nasville Miami Phoenix Nasville Miami

Picket Fence 20 80 0 30 0 0

Town House 15 60 0 35 0 0

Gentle Stream 10 30 35 50 0 0

El Presidente 25 20 75 65 0 0

Total Units transported 70 190 110 180 0 0

cost /unit 1450 725 2500 375 1675 2625



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Total cost 101500 137750 275000 67500 0 0 581750

The final cost of the transportation is $581750.

Question 5: Net profit of GSA for the year:

The following statement consolidates all the costs and revenues for the year from which we can determine the net profits.

Table 17:Net profit calculation for the year(after fixed cost and overheads)

Since it is given that whatever is produced by the firm will be sold because of favorable economic conditions, our revenues will be close to $ 8 million.

The transportation cost is as calculated in the previous question. The fixed costs and overheads are given.

We have a healthy profit of $2.4 million.

Model total units

gross profit in $

total gross profit in $

Picket Fence 130 9,600 1,248,000 Town House 110 11,520 1,267,200 Gentle Stream 125 15,360 1,920,000 El Presidente 185 19,200 3,552,000 Total Revenue 7,987,200 Transportation cost

581,750

Fixed cost 3,000,000 Over heads 2,000,000 Total cost 5,581,750 Net Profit 2,405,450



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Recommendations: If we meet the total demand by the distribution centers i.e.

Phoenix – 260

Nashville – 190

Miami – 340

Then the Gross Profit would be – 10,915,200

Our major constraint would of course be building additional capacity. There are two factors that we would need to consider. One is the cost of building and the other is time. The cost of building may not be that much of a hindrance as we have $2.4 million in profits and we would be able to raise additional funds because of our strong finances.

The other factor, time, will be more of an issue in our case. As no one can predict the future, we may not have an indication of the future economic conditions which could affect our predictions of the demand being as high as it currently is.



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Tables and figures:

Figures:


Figure 2: Consolidated diagram for all the possess and problems

Figure 3: Routes from El Cajon to distribution centers

Figure 4: All the routes cost calculation ) El Cajon to Distribution centers

Tables:

Table 1: building capacity for each model

Table 2: Transportation cost and time from El Cajon route to Distribution centers

Table 3: building allocation after B4 allocation

Table 4: Gross profit margin for all the models

Table 5: Total gross profit

Table 6: Allocation of the models to building at El Cajon Plant

Table 7: Sensitivity Analysis Report

Table 8: Consolidated minimum costs of transportation from El Cajon

Table 9: Transportaion cost (El Cajon to Distribution Centers)

Table 10: Transportaion cost (Elkhart to Distribution Centers)

Table 11:Supply and demand data for each of the models



Table 13: Allocation of units of Town House:



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Table 14: Allocation of units of Gentle Stream:

Table 15: Allocation of units of El Presidente:

Table 16: Consolidated transportation cost and allocation of the models:

Table 17:Net profit calculation for the year(after fixed cost and overheads)



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References: Stevenson, William J and Ozgur, Ceyhun. Introduction to Management Science with Spreadsheets. Tata McGraw-Hill

John A. Lawrence, Bary A. Pasternack, Applied Management Science, 2Nd Ed,Printed in india by brijbasi art press, Delhi

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